2024/02/22 by Will Barker, Sebastian Zell, Barker, Will +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2402.14917
openalex publication_date 2024/02/22 · openalex created_date 2024/02/27 · openalex updated_date 2026/07/28
It is well-known that the Einstein-Hilbert action exhibits a projective invariance in metric-affine gravity, generated by a single vector (just like diffeomorphisms). However, this symmetry offers no protection against formulating inconsistent models, e.g., with ghost and strong coupling problems. In this letter, we observe that non-minimal kinetic terms of Dirac spinors point to a new extended projective (EP) symmetry generated by a pair of vectors. We prove that the most general EP-invariant theory (at most quadratic in field strengths) is naturally free from all pathologies. Its spectrum only features the massless graviton and a single additional scalar field arising from the square of the Holst curvature. The scalar potential is suitable for inflation and our model moreover contains effective 4-Fermi interactions capable of producing fermionic dark matter. Finally, we point out an alternative double-vector symmetry that similarly leads to a healthy theory with a propagating vector field.